Abstract
We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.
Highlights
At large densities or small Bjorken-x, nonlinear QCD dynamics is expected to manifest itself in nuclear structure
The applied different phenomenological wave functions result in e.g., J=ψ production cross sections that differ up to ∼30% from each other [27,40,41]. This is a large model uncertainty, compared to the precise data that is already available from HERA and the LHC and especially given that the Electron Ion Collider (EIC) [42,43] is in the horizon
To reduce the model uncertainty related to the vector meson wave function, we propose in this work a new method to constrain the wave function for heavy mesons based on input from the nonrelativistic QCD (NRQCD) matrix elements
Summary
At large densities or small Bjorken-x, nonlinear QCD dynamics is expected to manifest itself in nuclear structure. The applied different phenomenological wave functions result in e.g., J=ψ production cross sections that differ up to ∼30% from each other [27,40,41] This is a large model uncertainty, compared to the precise data that is already available from HERA and the LHC and especially given that the Electron Ion Collider (EIC) [42,43] is in the horizon (and similar plans exist at CERN [44] and in China [45]). To reduce the model uncertainty related to the vector meson wave function, we propose in this work a new method to constrain the wave function for heavy mesons based on input from the nonrelativistic QCD (NRQCD) matrix elements These matrix elements capture nonperturbative long-distance physics and can be obtained by computing the vector meson decay widths in different channels as a systematic expansion in both the coupling constant αs and the quark velocity v.
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